No abstract

This paper studies the problem of the adaptive control of nonlinear impulsively coupled complex networks. Firstly, a class of adaptive controllers are designed for the nonlinear impulsive differential equations, where the nonlinear function can be decomposed into matching condition and mismatching condition. Secondly, combining with Lasalle invariant set theorem, Schur complement theorem and some inequality techniques, we consider the synchronization of impulsively coupled complex networks via the general adaptive control. Moreover, this paper proposes the pinning adaptive synchronization results for impulsive dynamical complex networks. Finally, the proposed results are verified by some examples in which simulations are available for comparison.

In this paper, the stability of familiar state constrained hybrid systems is considered. In the first, we prove the invariant set stability for the state constrained impulsive hybrid systems. Specifically, a robust control feedback method is applied for state constrained uncertain impulsive hybrid systems. With the auxiliary matrix assistance, some convergence criteria are derived to guarantee robust stability for state constrained uncertain hybrid systems with output disturbance by constructing the symmetric and asymmetric barrier Lyapunov functions (BLF), respectively. Finally, two comparative examples with simulations show that the proposed results are effective and superior.